Giá trị của $\large \lim\left[\dfrac{1}{n^2}+\dfrac{2}{n^2}+\dfrac{3}{

Giá trị của $\large \lim\left[\dfrac{1}{n^2}+\dfrac{2}{n^2}+\dfrac{3}{n^2}+...+\dfrac{n}{n^2}\right]$ bằng

• A.

  $\large \dfrac{1}{2}$

• B.

  $\large 0$

• C.

  $\large \dfrac{1}{3}$

• D.

  $\large 4$

Chọn D

Ta có: $\large \lim\left(\dfrac{1}{n^2}+\dfrac{2}{n^2}+\dfrac{3}{n^2}+...+\dfrac{n}{n^2} \right )=\lim\dfrac{1+2+3+...+n}{n^2}=\lim\dfrac{n(n+1)}{n^2}=\lim\left(\dfrac{1}{2}+\dfrac{1}{2n} \right )=\dfrac{1}{2}+0=\dfrac{1}{2}$